| Label |
Class |
Conductor |
Discriminant |
Rank* |
2-Selmer rank |
Torsion |
$\textrm{End}^0(J_{\overline\Q})$ |
$\textrm{End}^0(J)$ |
$\GL_2\textsf{-type}$ |
Sato-Tate |
Nonmaximal primes |
$\Q$-simple |
\(\overline{\Q}\)-simple |
\(\Aut(X)\) |
\(\Aut(X_{\overline{\Q}})\) |
$\Q$-points |
$\Q$-Weierstrass points |
mod-$\ell$ images |
Locally solvable |
Square Ш* |
Analytic Ш* |
Tamagawa |
Regulator |
Real period |
Leading coefficient |
Igusa-Clebsch invariants |
Igusa invariants |
G2-invariants |
Equation |
| 169.a.169.1 |
169.a |
\( 13^{2} \) |
\( - 13^{2} \) |
$0$ |
$0$ |
$\Z/19\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$6$ |
$0$ |
2.40.3, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(32.667031\) |
\(0.090490\) |
$[4,793,3757,-21632]$ |
$[1,-33,-43,-283,-169]$ |
$[-\frac{1}{169},\frac{33}{169},\frac{43}{169}]$ |
$y^2 + (x^3 + x + 1)y = x^5 + x^4$ |
| 196.a.21952.1 |
196.a |
\( 2^{2} \cdot 7^{2} \) |
\( - 2^{6} \cdot 7^{3} \) |
$0$ |
$2$ |
$\Z/6\Z\oplus\Z/6\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathrm{M}_2(\Q)\) |
|
$E_1$ |
|
|
|
$D_6$ |
$D_6$ |
$6$ |
$0$ |
2.360.3, 3.17280.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(1.000000\) |
\(11.777148\) |
\(0.109048\) |
$[1340,1345,149855,2809856]$ |
$[335,4620,90160,2214800,21952]$ |
$[\frac{4219140959375}{21952},\frac{6203236875}{784},\frac{12905875}{28}]$ |
$y^2 + (x^2 + x)y = x^6 + 3x^5 + 6x^4 + 7x^3 + 6x^2 + 3x + 1$ |
| 324.a.648.1 |
324.a |
\( 2^{2} \cdot 3^{4} \) |
\( - 2^{3} \cdot 3^{4} \) |
$0$ |
$0$ |
$\Z/21\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_3$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$6$ |
$0$ |
2.40.3, 3.1920.3 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(25.521769\) |
\(0.173617\) |
$[60,945,2295,82944]$ |
$[15,-30,140,300,648]$ |
$[\frac{9375}{8},-\frac{625}{4},\frac{875}{18}]$ |
$y^2 + (x^3 + x + 1)y = x^5 + 2x^4 + 2x^3 + x^2$ |
| 676.b.17576.1 |
676.b |
\( 2^{2} \cdot 13^{2} \) |
\( - 2^{3} \cdot 13^{3} \) |
$0$ |
$0$ |
$\Z/3\Z\oplus\Z/3\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathrm{M}_2(\Q)\) |
|
$E_1$ |
|
|
|
$D_6$ |
$D_6$ |
$0$ |
$0$ |
2.120.4, 3.17280.1 |
|
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(7.177121\) |
\(0.265819\) |
$[1244,1249,129167,2249728]$ |
$[311,3978,72332,1667692,17576]$ |
$[\frac{2909390022551}{17576},\frac{4602275343}{676},\frac{10349147}{26}]$ |
$y^2 + (x^2 + x)y = -x^6 + 3x^5 - 6x^4 + 6x^3 - 6x^2 + 3x - 1$ |
| 784.c.614656.1 |
784.c |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{4} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_3$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.5760.7 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(1.000000\) |
\(5.731485\) |
\(0.358218\) |
$[398,9016,912086,2401]$ |
$[796,2358,-2348,-1857293,614656]$ |
$[\frac{1248318403996}{2401},\frac{9291226221}{4802},-\frac{23245787}{9604}]$ |
$y^2 = x^5 - 4x^4 - 13x^3 - 9x^2 - x$ |
| 1296.a.20736.1 |
1296.a |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{4} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_3$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.1920.3 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(23.235042\) |
\(0.484063\) |
$[78,216,4806,81]$ |
$[156,438,-428,-64653,20736]$ |
$[4455516,\frac{160381}{2},-\frac{18083}{36}]$ |
$y^2 = x^5 - x^4 - 3x^3 + 4x^2 - x$ |
| 2187.a.6561.1 |
2187.a |
\( 3^{7} \) |
\( 3^{8} \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_3)$ |
|
✓ |
|
$C_2$ |
$D_6$ |
$3$ |
$1$ |
2.120.1, 3.5760.5 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(10.925677\) |
\(0.606982\) |
$[124,297,13275,3456]$ |
$[93,249,-239,-21057,6561]$ |
$[\frac{28629151}{27},\frac{2472653}{81},-\frac{229679}{729}]$ |
$y^2 + (x^3 + 1)y = -1$ |
| 2704.a.43264.1 |
2704.a |
\( 2^{4} \cdot 13^{2} \) |
\( 2^{8} \cdot 13^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.1440.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(11.781851\) |
\(0.736366\) |
$[110,520,15470,169]$ |
$[220,630,-620,-133325,43264]$ |
$[\frac{2013137500}{169},\frac{52408125}{338},-\frac{468875}{676}]$ |
$y^2 = x^5 - 5x^3 - 5x^2 - x$ |
| 2916.a.5832.1 |
2916.a |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{3} \cdot 3^{6} \) |
$0$ |
$0$ |
$\Z/3\Z\oplus\Z/3\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$D_6$ |
$4$ |
$0$ |
2.60.2, 3.17280.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(19.520681\) |
\(0.722988\) |
$[4,369,1257,-3072]$ |
$[3,-138,-356,-5028,-5832]$ |
$[-\frac{1}{24},\frac{23}{36},\frac{89}{162}]$ |
$y^2 + (x^3 + 1)y = x^3$ |
| 3721.a.3721.1 |
3721.a |
\( 61^{2} \) |
\( - 61^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$12$ |
$0$ |
2.40.3, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.007315\) |
\(28.081352\) |
\(0.205420\) |
$[196,6649,304573,-476288]$ |
$[49,-177,-187,-10123,-3721]$ |
$[-\frac{282475249}{3721},\frac{20823873}{3721},\frac{448987}{3721}]$ |
$y^2 + (x^3 + x + 1)y = -x^4 + x^3 + 3x^2 + x$ |
| 3969.b.35721.1 |
3969.b |
\( 3^{4} \cdot 7^{2} \) |
\( 3^{6} \cdot 7^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$18$ |
$0$ |
2.80.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.003155\) |
\(23.234167\) |
\(0.219945\) |
$[268,2961,216951,18816]$ |
$[201,573,-563,-110373,35721]$ |
$[\frac{1350125107}{147},\frac{57445733}{441},-\frac{2527307}{3969}]$ |
$y^2 + (x^3 + x + 1)y = -2x^5 + 3x^4 - 3x^2$ |
| 3969.c.35721.1 |
3969.c |
\( 3^{4} \cdot 7^{2} \) |
\( 3^{6} \cdot 7^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(12.485061\) |
\(0.780316\) |
$[268,2961,216951,18816]$ |
$[201,573,-563,-110373,35721]$ |
$[\frac{1350125107}{147},\frac{57445733}{441},-\frac{2527307}{3969}]$ |
$y^2 + (x^2 + x)y = x^5 - 5x^4 + 4x^3 - x$ |
| 5184.a.46656.1 |
5184.a |
\( 2^{6} \cdot 3^{4} \) |
\( - 2^{6} \cdot 3^{6} \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\mathrm{M}_2(\mathsf{CM})\) |
\(\mathsf{CM}\) |
✓ |
$J(C_2)$ |
|
✓ |
|
$C_2$ |
$D_6$ |
$2$ |
$0$ |
2.180.4, 3.8640.16 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(14.110203\) |
\(0.783900\) |
$[76,252,5160,24]$ |
$[228,654,-644,-143637,46656]$ |
$[\frac{39617584}{3},\frac{1495262}{9},-\frac{58121}{81}]$ |
$y^2 + x^3y = x^3 + 2$ |
| 6075.a.18225.1 |
6075.a |
\( 3^{5} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{2} \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_6)$ |
|
✓ |
|
$C_2$ |
$D_6$ |
$3$ |
$1$ |
2.120.1, 3.2880.4 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(15.574664\) |
\(0.865259\) |
$[164,2745,106365,-9600]$ |
$[123,-399,-409,-52377,-18225]$ |
$[-\frac{115856201}{75},\frac{9166493}{225},\frac{687529}{2025}]$ |
$y^2 + (x^3 + 1)y = x^3 + 1$ |
| 8281.b.405769.1 |
8281.b |
\( 7^{2} \cdot 13^{2} \) |
\( 7^{4} \cdot 13^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$12$ |
$0$ |
2.80.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.005669\) |
\(19.785401\) |
\(0.336475\) |
$[2596,375193,248614093,51938432]$ |
$[649,1917,-1907,-1228133,405769]$ |
$[\frac{115139273278249}{405769},\frac{524030063733}{405769},-\frac{803230307}{405769}]$ |
$y^2 + (x^3 + x + 1)y = -3x^5 + 9x^4 - 7x^3 - 2x^2 + x$ |
| 8281.c.405769.1 |
8281.c |
\( 7^{2} \cdot 13^{2} \) |
\( 7^{4} \cdot 13^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(19.785401\) |
\(1.236588\) |
$[2596,375193,248614093,51938432]$ |
$[649,1917,-1907,-1228133,405769]$ |
$[\frac{115139273278249}{405769},\frac{524030063733}{405769},-\frac{803230307}{405769}]$ |
$y^2 + (x^2 + x)y = x^5 + 8x^4 + 11x^3 + 3x^2 - x$ |
| 8649.b.700569.1 |
8649.b |
\( 3^{2} \cdot 31^{2} \) |
\( 3^{6} \cdot 31^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(5.541100\) |
\(1.385275\) |
$[1132,73377,21088959,369024]$ |
$[849,2517,-2507,-2115933,700569]$ |
$[\frac{1815232161643}{2883},\frac{19016091893}{8649},-\frac{200783123}{77841}]$ |
$y^2 + (x^2 + x)y = 9x^5 + 2x^4 - 21x^3 - 22x^2 - 8x - 1$ |
| 8649.c.700569.1 |
8649.c |
\( 3^{2} \cdot 31^{2} \) |
\( 3^{6} \cdot 31^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(18.772889\) |
\(1.173306\) |
$[1132,73377,21088959,369024]$ |
$[849,2517,-2507,-2115933,700569]$ |
$[\frac{1815232161643}{2883},\frac{19016091893}{8649},-\frac{200783123}{77841}]$ |
$y^2 + (x^2 + x)y = x^5 + 9x^4 + 13x^3 + 4x^2 - x$ |
| 11881.a.11881.1 |
11881.a |
\( 109^{2} \) |
\( 109^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(19.585813\) |
\(1.224113\) |
$[484,6649,988957,1520768]$ |
$[121,333,-323,-37493,11881]$ |
$[\frac{25937424601}{11881},\frac{589929813}{11881},-\frac{4729043}{11881}]$ |
$y^2 + (x^2 + x)y = x^5 - 3x^4 + 2x^2 - x$ |
| 12321.a.36963.1 |
12321.a |
\( 3^{2} \cdot 37^{2} \) |
\( - 3^{3} \cdot 37^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$12$ |
$0$ |
2.40.3, 3.480.12 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.007338\) |
\(18.952746\) |
\(0.417205\) |
$[4,6697,85285,-4731264]$ |
$[1,-279,-1107,-19737,-36963]$ |
$[-\frac{1}{36963},\frac{31}{4107},\frac{41}{1369}]$ |
$y^2 + (x^3 + x + 1)y = x^5 + 3x^4 + 4x^3 + 2x^2$ |
| 12544.a.12544.1 |
12544.a |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(18.675725\) |
\(1.167233\) |
$[62,112,2114,49]$ |
$[124,342,-332,-39533,12544]$ |
$[\frac{114516604}{49},\frac{5094261}{98},-\frac{79763}{196}]$ |
$y^2 = x^5 + 2x^4 - x^3 - 3x^2 - x$ |
| 12544.c.12544.1 |
12544.c |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(21.839889\) |
\(1.364993\) |
$[62,112,2114,49]$ |
$[124,342,-332,-39533,12544]$ |
$[\frac{114516604}{49},\frac{5094261}{98},-\frac{79763}{196}]$ |
$y^2 = x^5 - 2x^4 - x^3 + 3x^2 - x$ |
| 12544.i.614656.1 |
12544.i |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{4} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_3$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.2880.16 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(19.017610\) |
\(1.188601\) |
$[398,9016,912086,2401]$ |
$[796,2358,-2348,-1857293,614656]$ |
$[\frac{1248318403996}{2401},\frac{9291226221}{4802},-\frac{23245787}{9604}]$ |
$y^2 = x^5 + 4x^4 - 13x^3 + 9x^2 - x$ |
| 13689.a.13689.1 |
13689.a |
\( 3^{4} \cdot 13^{2} \) |
\( 3^{4} \cdot 13^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$12$ |
$0$ |
2.80.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.017079\) |
\(22.369055\) |
\(0.382039\) |
$[516,8073,1250613,1752192]$ |
$[129,357,-347,-43053,13689]$ |
$[\frac{441025329}{169},\frac{9461333}{169},-\frac{641603}{1521}]$ |
$y^2 + (x^3 + x + 1)y = x^5 - x^4 - 4x^3 - 2x^2$ |
| 13689.b.13689.1 |
13689.b |
\( 3^{4} \cdot 13^{2} \) |
\( 3^{4} \cdot 13^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(22.369055\) |
\(1.398066\) |
$[516,8073,1250613,1752192]$ |
$[129,357,-347,-43053,13689]$ |
$[\frac{441025329}{169},\frac{9461333}{169},-\frac{641603}{1521}]$ |
$y^2 + (x^2 + x)y = x^5 + 3x^4 + x^3 - 2x^2 - x$ |
| 15552.c.746496.1 |
15552.c |
\( 2^{6} \cdot 3^{5} \) |
\( 2^{10} \cdot 3^{6} \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_6)$ |
|
✓ |
|
$C_2$ |
$D_6$ |
$3$ |
$1$ |
2.120.1, 3.2880.4 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(8.616344\) |
\(0.957372\) |
$[142,1368,47940,-12]$ |
$[852,-2586,-2596,-2224797,-746496]$ |
$[-\frac{1804229351}{3},\frac{154259641}{72},\frac{3271609}{1296}]$ |
$y^2 + x^3y = 3x^3 + 8$ |
| 15876.b.222264.1 |
15876.b |
\( 2^{2} \cdot 3^{4} \cdot 7^{2} \) |
\( - 2^{3} \cdot 3^{4} \cdot 7^{3} \) |
$0$ |
$0$ |
$\Z/3\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_3$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$0$ |
$0$ |
2.40.3, 3.1920.3 |
|
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(5.070237\) |
\(1.690079\) |
$[636,6129,310743,28449792]$ |
$[159,798,16268,487452,222264]$ |
$[\frac{1254586479}{2744},\frac{2828663}{196},\frac{233147}{126}]$ |
$y^2 + (x^3 + x + 1)y = -x^6 + 2x^5 - 4x^4 + 4x^3 - 5x^2 + 2x - 1$ |
| 17689.a.17689.1 |
17689.a |
\( 7^{2} \cdot 19^{2} \) |
\( 7^{2} \cdot 19^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(15.833414\) |
\(0.989588\) |
$[580,11305,1902565,2264192]$ |
$[145,405,-395,-55325,17689]$ |
$[\frac{64097340625}{17689},\frac{1234693125}{17689},-\frac{8304875}{17689}]$ |
$y^2 + (x^2 + x)y = x^5 - 4x^4 + 2x^3 + x^2 - x$ |
| 17689.b.17689.1 |
17689.b |
\( 7^{2} \cdot 19^{2} \) |
\( 7^{2} \cdot 19^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$12$ |
$0$ |
2.80.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.020782\) |
\(23.059848\) |
\(0.479221\) |
$[580,11305,1902565,2264192]$ |
$[145,405,-395,-55325,17689]$ |
$[\frac{64097340625}{17689},\frac{1234693125}{17689},-\frac{8304875}{17689}]$ |
$y^2 + (x^3 + x + 1)y = -3x^4 - 3x^3 + x^2 + x$ |
| 18225.a.18225.1 |
18225.a |
\( 3^{6} \cdot 5^{2} \) |
\( - 3^{6} \cdot 5^{2} \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_6)$ |
|
✓ |
|
$C_2$ |
$D_6$ |
$4$ |
$0$ |
2.20.3, 3.2880.4 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.687921\) |
\(16.468178\) |
\(1.258756\) |
$[196,1305,73965,9600]$ |
$[147,411,-401,-56967,18225]$ |
$[\frac{282475249}{75},\frac{16117913}{225},-\frac{962801}{2025}]$ |
$y^2 + (x^3 + 1)y = 1$ |
| 20736.a.20736.1 |
20736.a |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{4} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_3$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.960.8 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(14.923707\) |
\(0.932732\) |
$[78,216,4806,81]$ |
$[156,438,-428,-64653,20736]$ |
$[4455516,\frac{160381}{2},-\frac{18083}{36}]$ |
$y^2 = x^5 + x^4 - 3x^3 - 4x^2 - x$ |
| 20736.f.186624.1 |
20736.f |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{6} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(7.834469\) |
\(1.468963\) |
$[74,288,5502,3]$ |
$[444,1302,-1292,-567213,186624]$ |
$[\frac{277375828}{3},\frac{10991701}{18},-\frac{442187}{324}]$ |
$y^2 = x^5 - 2x^4 - 9x^3 - 7x^2 - x$ |
| 20736.g.186624.1 |
20736.g |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{6} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(21.153445\) |
\(1.322090\) |
$[74,288,5502,3]$ |
$[444,1302,-1292,-567213,186624]$ |
$[\frac{277375828}{3},\frac{10991701}{18},-\frac{442187}{324}]$ |
$y^2 = x^5 + 2x^4 - 9x^3 + 7x^2 - x$ |
| 21316.a.42632.1 |
21316.a |
\( 2^{2} \cdot 73^{2} \) |
\( - 2^{3} \cdot 73^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$12$ |
$0$ |
2.40.3, 3.480.12 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.012306\) |
\(20.941659\) |
\(0.773095\) |
$[196,12337,588745,-5456896]$ |
$[49,-414,-908,-53972,-42632]$ |
$[-\frac{282475249}{42632},\frac{24353343}{21316},\frac{545027}{10658}]$ |
$y^2 + (x^3 + x + 1)y = 3x^3 + 4x^2 + x$ |
| 21904.e.350464.1 |
21904.e |
\( 2^{4} \cdot 37^{2} \) |
\( 2^{8} \cdot 37^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(20.051730\) |
\(1.253233\) |
$[302,5032,388574,1369]$ |
$[604,1782,-1772,-1061453,350464]$ |
$[\frac{314010903004}{1369},\frac{3067669341}{2738},-\frac{10100843}{5476}]$ |
$y^2 = x^5 + 3x^4 - 11x^3 + 8x^2 - x$ |
| 24649.a.24649.1 |
24649.a |
\( 157^{2} \) |
\( 157^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(23.312929\) |
\(1.457058\) |
$[676,17113,3248173,3155072]$ |
$[169,477,-467,-76613,24649]$ |
$[\frac{137858491849}{24649},\frac{2302387893}{24649},-\frac{13337987}{24649}]$ |
$y^2 + (x^2 + x)y = x^5 + 4x^4 + 3x^3 - x^2 - x$ |
| 26244.c.157464.1 |
26244.c |
\( 2^{2} \cdot 3^{8} \) |
\( 2^{3} \cdot 3^{9} \) |
$0$ |
$0$ |
$\Z/3\Z\oplus\Z/3\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$D_6$ |
$4$ |
$0$ |
2.60.2, 3.5760.3 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(1.000000\) |
\(14.148765\) |
\(1.572085\) |
$[60,945,2295,82944]$ |
$[45,-270,3780,24300,157464]$ |
$[\frac{9375}{8},-\frac{625}{4},\frac{875}{18}]$ |
$y^2 + (x^3 + 1)y = 2x^3$ |
| 26244.d.314928.1 |
26244.d |
\( 2^{2} \cdot 3^{8} \) |
\( 2^{4} \cdot 3^{9} \) |
$1$ |
$1$ |
$\Z/3\Z\oplus\Z/3\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_3)$ |
|
✓ |
|
$C_2$ |
$D_6$ |
$6$ |
$0$ |
2.20.3, 3.5760.3 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(0.985565\) |
\(12.739642\) |
\(1.395083\) |
$[24,189,1107,-162]$ |
$[72,-918,-3024,-265113,-314928]$ |
$[-6144,1088,\frac{448}{9}]$ |
$y^2 + y = x^6 - 2x^3$ |
| 26244.e.472392.1 |
26244.e |
\( 2^{2} \cdot 3^{8} \) |
\( - 2^{3} \cdot 3^{10} \) |
$0$ |
$0$ |
$\Z/3\Z\oplus\Z/3\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_3)$ |
|
✓ |
|
$C_2$ |
$D_6$ |
$4$ |
$0$ |
2.20.3, 3.5760.3 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(1.000000\) |
\(12.048083\) |
\(1.338676\) |
$[356,3969,419553,248832]$ |
$[267,1482,-2884,-741588,472392]$ |
$[\frac{5584059449}{1944},\frac{174127343}{2916},-\frac{5711041}{13122}]$ |
$y^2 + (x^3 + 1)y = 2$ |
| 32761.a.32761.1 |
32761.a |
\( 181^{2} \) |
\( - 181^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$12$ |
$0$ |
2.40.3, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.020993\) |
\(24.533253\) |
\(0.515025\) |
$[676,41449,6681253,-4193408]$ |
$[169,-537,-547,-95203,-32761]$ |
$[-\frac{137858491849}{32761},\frac{2591996433}{32761},\frac{15622867}{32761}]$ |
$y^2 + (x^3 + x + 1)y = x^5 + 10x^2 + 19x + 10$ |
| 37636.a.602176.1 |
37636.a |
\( 2^{2} \cdot 97^{2} \) |
\( - 2^{6} \cdot 97^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$12$ |
$0$ |
2.40.3, 3.480.12 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.021512\) |
\(15.407337\) |
\(0.994336\) |
$[196,28033,1517953,-77078528]$ |
$[49,-1068,-4912,-345328,-602176]$ |
$[-\frac{282475249}{602176},\frac{31412283}{150544},\frac{737107}{37636}]$ |
$y^2 + (x^3 + x + 1)y = x^5 + 4x^4 + 6x^3 + 3x^2$ |
| 38416.a.614656.1 |
38416.a |
\( 2^{4} \cdot 7^{4} \) |
\( 2^{8} \cdot 7^{4} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathrm{M}_2(\Q)\) |
|
$E_1$ |
|
|
|
$D_6$ |
$D_6$ |
$6$ |
$0$ |
2.240.2, 3.8640.13 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.022206\) |
\(19.017610\) |
\(1.266932\) |
$[398,9016,912086,2401]$ |
$[796,2358,-2348,-1857293,614656]$ |
$[\frac{1248318403996}{2401},\frac{9291226221}{4802},-\frac{23245787}{9604}]$ |
$y^2 = x^6 - 3x^5 - x^4 + 7x^3 - x^2 - 3x + 1$ |
| 43264.c.43264.1 |
43264.c |
\( 2^{8} \cdot 13^{2} \) |
\( 2^{8} \cdot 13^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.1440.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(23.105046\) |
\(1.444065\) |
$[110,520,15470,169]$ |
$[220,630,-620,-133325,43264]$ |
$[\frac{2013137500}{169},\frac{52408125}{338},-\frac{468875}{676}]$ |
$y^2 = x^5 - 5x^3 + 5x^2 - x$ |
| 46656.c.93312.1 |
46656.c |
\( 2^{6} \cdot 3^{6} \) |
\( 2^{7} \cdot 3^{6} \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_6)$ |
|
✓ |
|
$C_2$ |
$D_6$ |
$4$ |
$0$ |
2.20.3, 3.8640.14 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.664878\) |
\(8.473201\) |
\(1.877882\) |
$[44,9,357,48]$ |
$[132,672,-1264,-154608,93312]$ |
$[\frac{1288408}{3},\frac{149072}{9},-\frac{19118}{81}]$ |
$y^2 + x^3y = x^3 - 1$ |
| 48841.b.830297.1 |
48841.b |
\( 13^{2} \cdot 17^{2} \) |
\( - 13^{2} \cdot 17^{3} \) |
$0$ |
$0$ |
$\mathsf{trivial}$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$0$ |
$0$ |
2.40.3, 3.480.12 |
|
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(4.401272\) |
\(4.401272\) |
$[764,10777,650195,106278016]$ |
$[191,1071,30923,1189813,830297]$ |
$[\frac{254194901951}{830297},\frac{438975873}{48841},\frac{3903467}{2873}]$ |
$y^2 + (x^3 + x + 1)y = -x^6 + 2x^5 - 5x^4 + 6x^3 - 6x^2 + 2x - 1$ |
| 52441.a.52441.1 |
52441.a |
\( 229^{2} \) |
\( 229^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(22.932231\) |
\(1.433264\) |
$[964,41449,10706437,6712448]$ |
$[241,693,-683,-161213,52441]$ |
$[\frac{812990017201}{52441},\frac{9700282053}{52441},-\frac{39669323}{52441}]$ |
$y^2 + (x^2 + x)y = x^5 + 5x^4 + 5x^3 - x$ |
| 59049.a.177147.1 |
59049.a |
\( 3^{10} \) |
\( 3^{11} \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_3)$ |
|
✓ |
|
$C_2$ |
$D_6$ |
$4$ |
$0$ |
2.20.3, 3.5760.8 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.712785\) |
\(8.055321\) |
\(1.913904\) |
$[52,-63,-111,384]$ |
$[117,783,-2079,-214083,177147]$ |
$[\frac{371293}{3},\frac{63713}{9},-\frac{13013}{81}]$ |
$y^2 + (x^3 + 1)y = x^3 - 1$ |
| 62208.n.746496.1 |
62208.n |
\( 2^{8} \cdot 3^{5} \) |
\( 2^{10} \cdot 3^{6} \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_6)$ |
|
✓ |
|
$C_2$ |
$D_6$ |
$3$ |
$1$ |
2.120.1, 3.2880.3 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(8.616344\) |
\(1.436057\) |
$[142,1368,47940,-12]$ |
$[852,-2586,-2596,-2224797,-746496]$ |
$[-\frac{1804229351}{3},\frac{154259641}{72},\frac{3271609}{1296}]$ |
$y^2 = x^6 - 3x^3 + 2$ |
| 72900.a.291600.1 |
72900.a |
\( 2^{2} \cdot 3^{6} \cdot 5^{2} \) |
\( - 2^{4} \cdot 3^{6} \cdot 5^{2} \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_6)$ |
|
✓ |
|
$C_2$ |
$D_6$ |
$4$ |
$0$ |
2.20.3, 3.2880.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.563877\) |
\(10.315182\) |
\(1.938833\) |
$[184,1845,87015,150]$ |
$[552,1626,-1616,-883977,291600]$ |
$[\frac{13181630464}{75},\frac{211024448}{225},-\frac{3419456}{2025}]$ |
$y^2 + y = x^6 - 2x^3 + 1$ |
| 72900.b.291600.1 |
72900.b |
\( 2^{2} \cdot 3^{6} \cdot 5^{2} \) |
\( - 2^{4} \cdot 3^{6} \cdot 5^{2} \) |
$0$ |
$0$ |
$\Z/3\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_6)$ |
|
✓ |
|
$C_2$ |
$D_6$ |
$2$ |
$0$ |
2.20.3, 3.8640.7 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(10.315182\) |
\(1.146131\) |
$[184,1845,87015,150]$ |
$[552,1626,-1616,-883977,291600]$ |
$[\frac{13181630464}{75},\frac{211024448}{225},-\frac{3419456}{2025}]$ |
$y^2 + x^3y = 2x^3 + 5$ |
